# Finding heat lost when waters of different temps. Are mixed

1. Nov 5, 2013

### astru025

1. The problem statement, all variables and given/known data

90 grams of water at 75°C are mixed with an equal amount of water at 25°C in a completely insulated container. The final temperature of the water is 50°C. How much heat is lost by the hot water?

2. Relevant equations

The hot water drops to 50 degrees Celsius so it has lost 25 degrees celsius. My answer needs to be in calories though and I'm not sure where to go from here. How do I get 25 degrees Celsius to calories?

3. The attempt at a solution
My attempt is written above.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 5, 2013

3. Nov 5, 2013

### Legaldose

Well, the heat lost by the water will be measured in units of energy, not temperature as you may think. Do you remember this guy?

$$Q=mc_{w}\Delta T$$

4. Nov 5, 2013

### nil1996

You need specific heat capacity of water.SpecificHeat capacity of water is 1 calorie/gram °C.So from this you can work out the heat given out by the hot water as its temperature falls.

5. Nov 5, 2013

### astru025

Okay thank you very much! My book is very light on math/ equations, I had never seen that Q=mcT equation before... I took 1 cal/gram x 90 grams x 25 degrees. I got 2250 cal which proved to be correct! Thanks very much